Analog experiments of lava flow emplacement

Laboratory experiments that simulate lava flows have been in use by volcanologists for many years. The behavior of flows in the lab, where “eruption” parameters, material properties, and environmental settings are tightly controlled, provides insight into the influence of various factors on flow evolution. A second benefit of laboratory lava flows is to provide a set of observations with which numerical models of flow emplacement can be tested. Models of lava flow emplacement vary in mathematical approach, physical assumptions, and computational cost. Nonetheless, all models require thorough testing and evaluation, and laboratory experiments produce an excellent test for models. This paper provides a primer on modern analog laboratory lava flow experiments. It reviews scaling con- siderations and provides quantitative information meant to guide future experimentalists in designing their experiments to be relevant to natural processes. Traditional and novel laboratory techniques are described, including a discussion of current limitations. New insights from recent experiments highlight the impact of topographic conditions and highlight the importance of considering bed roughness, major obstacles, and slope breaks. The influence of episodic or non-uniform effusion rate is demonstrated through recent experi- mental works. Lastly, the paper discusses several open questions about lava flow emplacement and the ways in which future improvements in experimental methods, such as the ability to utilize three-phase suspensions and materials with complex rheologies and to image the interior of flows could help answer these.


Motivation
Lava flows present a hazard to infrastructure and human lives, as demonstrated recently by flows in Hawai'i (Patrick et al., 2017), Cape Verde (Jenkins et al., 2017) and elsewhere.At the same time lava flows cover vast areas on Earth and other planets and moons, and therefore record a long history of planetary evolution and tectonic processes (e.g., Wilson and Head, 1983;Head et al., 1992).Deciphering the factors that control how lava flows form and evolve (e.g., Manga and Ventura, 2005;Harris et al., 2016) is key to understanding these landscapes.
After many years of scientific study of lava flow emplacement, the basic understanding of the controlling factors has been established: Lava flow paths depend on the ground slope, the rheology of the lava, and the cooling conditions (e.g., Griffiths, 2000).These factors have consequently been included in numerical flow models, the key tools used to assess lava flow hazard (e.g., Bilotta et al., 2016;Cappello et al., 2015;Harris et al., 2016;Hidaka et al., 2005;Kelfoun and Vargas, 2015;Tarquini et al., 2010).However, there are still many aspects of flow behavior that are observed in nature but are not currently included in simulation models.These include processes such as flow inflation and breakout, levee and channel formation, and the interaction of flows with bed roughness or vegetation.Many existing simulation models also do not consider the impact of non-constant effusion rate, the impact of turbulence, or thermal or mechanical erosion of the substrate.
of scale factors and dimensional analysis is also given by Kavanagh et al. (2018) as part of their review of experimental and numerical models in volcanology.This paper focuses on the scaling considerations most relevant for lava flow emplacement simulations.It introduces the mathematical definition of these numbers, and provides values for the relevant physical constants that construct them, to calculate typical ranges of the numbers for experiments and natural systems.Table 1 provides the definitions, units and typical values for material properties and conditions relevant for scaling of analog laboratory lava flow models.The following list gives a more detailed description of several non-dimensional numbers relevant to analog models of lava flows: The Péclet number, the Reynolds number, the flow regime parameter, the Deborah number, and the Bingham number.
• Péclet number, P e -states the ratio of heat transfer by fluid advection to heat transfer by thermal conduction, and is expressed as UL  , where U is the mean flow velocity, L is a characteristic length scale (usually taken as the thickness of the flow), and  is the thermal diffusivity of the lava.A

P e
1 means that the flow is moving fast enough to advect its heat and not conduct it away.If P e ⌧ 1 a flow will cool and solidify before it moves.
Values of  for natural lavas depend on the vesicularity (Robertson and Peck, 1974;Keszthelyi, 1994), but are usually in the range of 3 7 ⇥ 10 7 m 2 /s (e.g., Neri, 1998).Flow speeds and thicknesses for basaltic lava vary widely between slow moving pāhoehoe toes, where U =0.01-1 m/s and L =0.3-3 meters (Hon et al., 1994;Gregg et al., 2004)] and larger flows, with speeds of < 1 m/s for 'a'a and up to 20 m/s for fast channelized flows, and flow thickness of up to 20 meters (Cashman et al., 1999;Lipman and Banks, 1987).These values give P e on the order of 10 3 for a pāhoehoe toe, and on the order of 10 8 for a channelized flow.Lava flows that have more evolved compositions are thicker and move more slowly.For example, Farquharson et al. (2015) reported surface velocities of 3.57⇥10 5 m/s for the ⇡ 30 m thick flow at Cordon-Caulle.The corresponding thermal diffusivity of a rhyolite is 5.5⇥10 7 m 2 /s, giving P e = 1.9 ⇥ 10 3 (Romine et al., 2012), similar to pāhoehoe toes.Hence, P e for natural flows is always much greater than 1.Typical laboratory flows are thinner (0.05-0.1 meters) and slower (0.5-5 mm/s (Fink and Griffiths, 1990;Dietterich et al., 2015;Rumpf et al., 2018)).Thermal diffusivities of materials commonly used in the laboratory range from 8.16⇥10 8 for polyethylene glycol (PEG) (Manufacturer data sheet) to 1.9⇥10 7 for corn syrup (NOAA CAMEO Chemicals website).Therefore, the P e for laboratory flows is also well above 1, keeping them safely in the advection-dominated regime.
• Reynolds number, Re -measures the ratio of inertial forces to viscous forces in the flow, and sets the degree to which a flow is laminar or turbulent.Re is calculated as ⇢UL ⌘ , where ⇢ is the fluid's density and ⌘ is the fluid's kinematic viscosity.Flow in an open channel is considered laminar for Re < 500 and turbulent for Re > 2000.With viscosities as high as 10 10 Pa s, Re for most lava flows is typically within the laminar regime.Basalt flows, the most common low viscosity lavas, can sometimes straddle the laminar-turbulent boundary.For instance, the Re for a high-flux Hawaiian flow that is 10 meters thick, moving at 10 m/s, with a density of 2000 kg/m 3 (⇡30% vesicularity) and a viscosity of 100 Pa s, is 2,000, the cut-off between transitional to fully turbulent flow.Komatiite flows (viscosity of 0.1-1 Pa s) may have been fully turbulent.Because the viscosity of laboratory materials is easily controlled (for example through changes in temperature or chemical composition) they can be in either flow regime.It is important therefore to know what kind of lava flows the laboratory experiments are simulating and select the appropriate experimental parameters and material properties combination.a • Flow regime parameter, -A popular scaling parameter for volcanological application, (Fink and Griffiths, 1990;Gregg and Keszthelyi, 2004), represents the ratio between t s , the amount of time required for a crust to form at the flow surface, and t a , the time it takes to advect heat to a distance equivalent to the flow depth, taken as the maximum flow velocity divided by the flow depth. is defined as ts ta (Fink and Griffiths, 1990;Gregg and Fink, 2000;Gregg and Keszthelyi, 2004).Values of distinguish between regimes that correspond to different flow morphologies: High values indicate that a flow moves faster than it has time to form a crust, and therefore the corresponding flows will have disrupted surfaces.Quantitatively, >30 corresponds to leveed flows and >9 to cracked and broken lava toes.Low values, on the other hand, correlate with tube formation and inflated toes.Robertson and Kerr (2012) and Lev and James (2014) include a detailed script for calculating for both natural and laboratory flows using the material properties, flow velocity, and environmental conditions.
A related characterization is given by Griffiths et al. (2003), who define the parameter # = (R a /R 0 ) 1 3 , where R a is the Rayleigh number for convection within the flow, and R 0 is taken to be equal to 100 Griffiths et al. (2003).# < 25 indicates a likely development of a solid roof and a tube regime, while # > 25 leads to a mobile crust and an open channel flow.
• Deborah number, De -expresses the fluidity of a material by comparing the time scale of observation t o with the timescale of stress relaxation t r (Reiner, 1964).De, defined as t r /t o , is relevant in particular when using non-Newtonian liquids.For a purely viscous fluid, the relaxation time is zero, and for a perfect spring, it is infinite.For a viscoelastic material (a Maxwell body) t r is the ratio of its viscosity to Young's modulus.If the observation time is much shorter than the relaxation time (De 1), the material behaves like a solid; if the observation time is much longer, (De ⌧ 1) the viscous behavior dominates.For most lavas, viscous behavior dominates on the flow time and length scales, meaning De ⌧ 1.However, if the lava forms a foam, such as the case at a lava lake or a reticulite-forming fountain, viscoelasticity becomes important (Spina et al., 2016).In addition, a viscoelastic layer is sometimes present below a solid crust at the surface of the flow (Hon et al., 1994;Lore et al., 2000;Stovall et al., 2009).Therefore, an appropriate observation time needs to be chosen for the experiment depending on the process of interest (flow advance, crust formation, bubble coalescence...) and the chosen material.
• Bingham number, B -reflects the relative importance of yield stress y and viscosity ⌘ for a characteristic strain rate ✏: B = y ✏⌘ (Griffiths, 2000).Lavas, in particular when highly crystalline, are often considered to be Bingham or Herschel-Bulkley materials, where y >0 (McBirney and Murase, 1984).Depending on the situation, B can be much larger or much smaller than unity.An analog material should be selected to have a similar B to that of the simulated lava system.For instance, the highly crystalline lava dome that erupted at Soufrière Hills, Montserrat, had a B⇡10 4 (Griffiths, 2000), and a purely viscous material such as syrup would not be an appropriate analog.Instead, a clay slurry with a non-zero yield stress would be better (B for the clay-PEG slurry domes in the experiments of Griffiths and Fink (1997) was ⇡ 10 5 , given 0 = 84 Pa, ⌘=0.8 Pa s, and strain rate ✏ ⇡10 3 s 1 ).A large, crystal-poor, basaltic channel flow, on the other hand, would have B ⌧ 1, and can be simulated with syrup.

Materials
The choice of materials to use in a laboratory flow experiment depends on the process of interest, as well as on availability and practicality.Past laboratory flow experiments chose materials which emphasized different aspects of lava rheology, depending on the study's focus.For example, sugar-based syrups and silicone oils are simple and cheap simulants of isothermal or temperature-dependent viscous flow regimes (Dietterich et al., 2015;Garel et al., 2015).Silicone covered in sand and flour has been used by Buisson and Merle (2005) to mimic flows with a brittle crust.Polyethylene glycol (PEG) has been used extensively to simulate solidification (e.g., Fink and Griffiths, 1990;Soule and Cashman, 2004;Garel et al., 2014;Rumpf et al., 2018), and the plastic Bingham rheology of kaoline slurries was utilized to simulate the growth of highly crystalline lava domes (Blake, 1990).
Recently, several works have negated the need to approximate lava properties with an analog by using molten basalt in large scale experiments.Currently, two US facilities, located at Syracuse University and at the University of Buffalo, perform such experiments.Lev et al. (2012) used molten basalt experiments to extract lava rheological parameters from the surface velocities of a lava flow.Edwards et al. (2013) and Oddsson et al. (2016) studied heat transfer between lava and over-or under-lying bed of ice or snow.Nonetheless, even when using molten natural rocks, there are still differences with natural lavas, for example vesicularity, crystallinity, cooling rates and crust formation.
A wealth of information exists on industrial materials that can be used for laboratory experiments, e.g. on websites, engineering handbooks, and manufacturer information sheets.One important resource is a newly developed website, a product of the European NEMOH Marie Curie Training Network.The site, located at https://sites.google.com/site/volcanologyanalogues/home,contains information about common and more unusual materials used for volcanology-related laboratory experiments, including PEG, syrup, silicone, resin, and others.While published information is essential for planning and material selection, it is important that scientists measure the properties of the actual materials they use in experiments.There can always be a "bad batch", slurries might settle, syrup might dehydrate, PEG may have a somewhat different grade than labeled, and so on.

Tools and techniques
An experimental fluid mechanics laboratory comes with requirements, some more straight-forward than others.A water source and sink, electricity, and temperature control are needed.Other essentials include scales, heaters and freezers, thermometers/thermocouples, glassware and tanks.Windows are not desired, as external light can interfere with imaging, in particular when experiments are performed under water, as with PEG. Figure 1 shows examples of experimental environments.
A key component of conducting experiments is careful documentation.Cameras, both still and video, are the most common way to document experiments.Thermal infrared cameras such as FLIR (Forward-Looking Infrared) cameras are useful for collecting spatial temperature information throughout an experiment.Notable novel techniques for collecting data in laboratory experiments include sheet laser lighting (Andrews, 2014), which can see through transparent flows, and laser scanners that provide high-resolution topographic data of flow structure (Starek et al., 2011).
Data collected by cameras can be analyzed both manually and automatically using computer vision tools, to extract information about the evolution of each flow over the course of the experiments.Analysis can include tracking the flow front position and the flow width or thickness over time (e.g., Blake, 1990;Balmforth et al., 2000), as these are observables that are directly comparable with predictions from analytical or numerical models (Cordonnier et al., 2015;Dietterich et al., 2017).A more complete dataset on the velocity distribution of the flow surface can be obtained using techniques such as Particle Image Velocimetry (PIV) (e.g., Applegarth et al., 2010) or Optical Flow (e.g., Horn and Schunck, 1981;Lucas and Kanade, 1981;Lev et al., 2012).Both techniques produce comparable results, but have different strengths and weaknesses.PIV requires that a sufficient number of seeded particles are available for tracking, and care must be taken that these particles do not interfere with the flow properties.The density of the particles should match that of the fluid, to prevent sinking/floating.In addition, particles embedded in a transparent liquid and moving towards/away from the camera may appear to be moving laterally due to parallax, and thus introduce error into the measured flow field.Optical Flow assumes that the brightness of moving objects stays constant between frames.This assumption, called the "brightness constancy constraint" states that the brightness I(x, y, t) of a pixel at position (x, y) and time t will be equal to I(x + x, y + y, t + t).These constraints translates to the so called Optical Flow equation: @I @t + @I @x V x + @I @y V y = 0 , where V x , V y are the velocities in the x and y directions.Because the Optical Flow equation has two unknowns, such methods require additional constraints on the solution.These constraints can attempt, for example, to maximize the overall smoothness of the solution (Horn and Schunck, 1981), to match velocities within a certain size window (Lucas and Kanade, 1981), or to use a polynomial to express the brightness in a pixel neighborhood (Farnebäck, 2003).
Photographic documentation of experiments can also yield information on flow topography and morphology, in addition to its kinematics.Photogrammetry techniques such as Structure-from-Motion (SfM) now provide simple and efficient means to construct high-resolution digital surface models of experimental products through readily available software tools (e.g., PhotoScan©, Pix4D©, and VisualSFM).The introduction of synchronized camera arrays to volcanology experiments (Dietterich et al., 2015;Guldstrand et al., 2018) allows capturing of three-dimensional flow morphology throughout the duration of an experiment, producing even more quantitative data that models should comply with.Figure 2 shows observations from the molten basalt obstacle experiments, including a velocity field obtained using Optical Flow (Figure 2a), a temperature distribution as observed by a FLIR camera (Figure 2b), and a flow topography map calculated using SfM (Figure 2c).An additional way to collect high-resolution topographic and roughness information on the flow surface is to use low-cost laser scanners such as the Kinect© sensor.The advances in collecting high-resolution quantitative information on flow morphology, both in the laboratory and in nature, provide a rich new dataset to compare with models.

Three decades of analog flow models
The field of analog laboratory experiments for lava flow studies was very active in the late 1990s and early 2000s, with the most noteworthy of those being the works by Fink and Griffiths (1990); Fink (1992); Fink and Griffiths (1998); Griffiths and Fink (1997) and Sakimoto and Gregg (2001).These early works focused on the fundamental processes of flow advance and solidification, and identified the different regimes that result from the competition between these processes.Relationships between the rates of flow advance, effusion and cooling/crust formation have been defined in that time, and the impact on flow structure and morphology was recognized (Balmforth et al., 2006;Blake and Bruno, 2000;Griffiths and Fink, 1997;Costa and Macedonio, 2005;Osmond and Griffiths, 2001).In the later 2000s, emphasis shifted to studying the impact of channels, either pre-existing channels of various shapes (Cashman et al., 2006;Takagi andHuppert, 2007, 2008) or self-forming channels resulting from levee solidification (Kerr et al., 2006).
More recent works have begun to examine more closely the impact of rheology.Robertson and Kerr (2012) built upon the studies from the 1990s and used wax-kaolin slurries to quantify the impact of non-Newtonian rheology on the solidification of a crust.Castruccio et al. (2014) looked at how flows of twophase mixtures (sugar suspensions) behaved in a channel, and Applegarth et al. (2010) included a brittle crust at the top of their silicone-based flows.Longo et al. (2015) revisited the question of the impact of channel shapes on flow, this time using non-Newtonian materials.Other works have focused on flow cooling, particularly how it is sensed remotely by satellite or airborne thermal cameras (Garel et al., 2013(Garel et al., , 2014;;Robertson and Kerr, 2012).Table 2 lists important experimental works from the past three decades.For each reference, the table details the materials and configuration of the experiment, its central goal, and the observable data reported in the paper.This table serves as a reference guide to past experimental works.

Recent advances in analog lava flows
Recently, attention has turned to using experiments to study the impact of topography of various length scales on flow evolution (Dietterich et al., 2015;Rumpf et al., 2018), perhaps in response to the ever increasing availability of high-resolution topography data for volcanic regions (e.g., Deardorff and Cashman, 2012;Deligne et al., 2016).Other recent works have looked at the effect of time variability in effusion rates (Rader et al., 2017) and of more complex rheologies (Castruccio et al., 2014;Závada et al., 2009) on flow evolution.This section highlights notable recent works as examples for the insights volcanologists gain from laboratory experiments into outstanding questions regarding flow emplacement.

Unsteady flow dynamics
Unsteady flow dynamics, which includes a time variable effusion of lava, lava flow inflation, and flow breakouts, are frequently observed during eruptions (e.g., Walker, 1971;Hon et al., 1994;Self et al., 1996).However, these fundamental processes have been difficult to implement in numerical models, for instance because they require changing the computational mesh or handling a moving free surface.The physical understanding of lava flow inflation and breakouts is still lacking, and models either ignore these processes completely (e.g., Harris and Rowland, 2015;Kelfoun and Vargas, 2015;Tarquini et al., 2010) or include it through a stochastic approach (Hamilton et al., 2013).It is situations like these that analog experiments have shown their power.For example, Blake and Bruno (2000) examined the impact of flux and viscosity on the timing of breakouts.
Recent work by Rader et al. (2017) used the ability to control effusion rate provided by the laboratory setting to examine the possibility that pulsating effusion can create lava flows with wider extent than steady effusion with the same total volume production.Rader et al. (2017) used PEG and carefully calibrated effusion rates and cooling timescales to demonstrate how pulsating leads to inflation and breakout.Figure 3  (a, b) show photos of two representative experiments; the photos demonstrate the stages of inflation and the difference between steady and pulsating effusion cases.This was a classic demonstration of the benefit of analog experiments to examine difficult-to-model processes.This experimental dataset will be an excellent test for future, more sophisticated flow simulation codes.
Unsteady and episodic effusion has been documented repeatedly for lava domes around the world (Bluth and Rose, 2004;Harris et al., 2003;Loughlin et al., 2010;Odbert et al., 2014;Nakada et al., 1999).Because the viscous spreading timescales for domes are similar to or longer than the timescales for changes in effusion rates, time variations in effusion are likely to impact dome structure and stability.Wegleitner and Lev (2018) experimented with clay+PEG slurries and demonstrated that more episodic effusion led to rough, broken dome surfaces, compared to smooth, largely intact surfaces for constant effusion rates (Figure 3 c-h).This observation contributes to hazard assessment for dome collapse, since it has been shown that a dome that grows episodically and develops more damaged surface may be less stable, as well as more prone to weakening by hydrothermal alteration (Ball et al., 2013).

Experiments on the impact of topography
Lava flows naturally interact with the topography of the ground over which they are flowing.A first order parameter is the overall slope of the ground, which sets the main force driving the flow downhill.Secondary to the overall slope, several topographical factors impact flow evolution, including flow-scale obstacles (or, more generally, a sharp change of slope from negative to positive), small-scale variability of the ground, slope breaks (rapid steepening or shallowing of the along-flow slope) and lateral confinement by positive topography.Several recent works quantified the influence of the above factors on flow emplacement using lab experiments with analogs and molten basalt.

Obstacles
Many lava flows interact with steep obstacles along their path which can divert, split or confine the flow.These obstacles may be natural, such as fault scarps or a thick past flow, or human-made such as buildings.Especially in the case of buildings, such obstacles are not always large enough to be within the resolution of the digital elevation models (DEMs) used as input for flow emplacement models.Sometimes obstacles are constructed during an eruption, to divert a flow's path away from a community or important facility (Barberi et al., 2004;Colombrita, 1984;Williams, 1983) and are thus not part of the pre-eruption DEM.However, it is important to understand how such obstacles influence flows, for instance by causing thickening upslope of the obstacle, and changing flow's advance rate (Wolfe, 1988).Dietterich et al. (2015) showed that the orientation of a wall (linear vertical obstacle) relative to the flow direction impacts the amount of inflation behind the obstacle and the change in flow advance rate.A similar relation was observed for V-shaped obstacles, where the opening angle impacted flow thickening and speed (Figure 2).The experiments reported by Dietterich et al. (2015) were performed using sugar syrup (a Newtonian, isoviscous fluid) and molten basalt.The results from the experiments have already been used as a benchmark test to numerical flow models, as summarized by Dietterich et al. (2017).Flow inflation behind an obstacle appeared to be a challenge for most codes tested, yet its importance cannot be overstated, especially in the context of flow hazard mitigation and flow diversion.Figure 2c shows the topography of a molten basalt flow as it thickened behind an obstacle; the topography was produced through SfM on data from an array of 10 synchronized cameras placed around the experiment (Dietterich and Dietrich, in review).
Syrup and thin molten basalt experiments don't capture an important process in lava flows -the formation of a solid crust at the cooling flow surface above a still-molten interior.Therefore, an additional sequence of experiments was performed, using PEG.The results, shown in Figure 4, indicated that the degree of flow thickening above a V-shaped obstacle for all three materials used depends on the opening angle of the obstacle.The behavior of PEG was similar to that of the Newtonian isoviscous syrup, despite the formation of a solid crust on the PEG flows.Basaltic flows thickened to a greater degree, pointing to a greater influence of temperature-dependent viscosity compared with a solid crust.Such observations in the lab can guide priorities in improving numerical models, depending on the application (e.g., barrier design).Since obstacles that could be important for flows are often not represented in DEMs, models will need to include them explicitly through, perhaps, a local refinement of computational grids or a local artificial modification of the DEM.

Small-scale bed roughness
At the other end of the spectrum of topographical variations, bed roughness refers to topographical variations with an amplitude less than half a typical flow thickness.Anecdotal field observations from Kīlauea, Hawai'i and similarly low-relief terrains indicate that the underlaying roughness impacts flows' lateral extent and advance rate (and thus their cooling and morphology).Intuitively one can imagine that a flow would move slower on a rough surface.However, to date, no flow simulation code considers the influence of bed roughness on flow advancement; only topographic variations large enough to be captured by the digital elevation model being used, and with the vertical amplitude of similar or larger to that of the typical flows, are considered.Rumpf et al. (2018) performed a series of experiments using corn syrup, PEG and molten basalt.Liquids were extruded onto substrates with amplitude-specific roughness, set by the grain size of the substrate cover material (sand, gravel, pebbles, etc).Figure 5 displays overhead views of a sub-group of the experiments, spanning a range of bed roughness values and flow materials.The photos reveal the impact of bed roughness on flow outline complexity, with rougher (larger grain size) beds causing more irregular perimeters and promoting breakouts.The experiments were analyzed for flow front advance rate over time.The results, shown in Figure 6, were consistent among all three liquids tested and showed that increasing grain size led directly to a reduction in flow advance rate.The slowing down of flow advance is equivalent to an increase in the apparent viscosity of the liquid, yet the amount of that increase depended on grain size and liquid properties.The results provide a simple way for numerical flow models, and in particular fast probabilistic models, to incorporate information about pre-existing small-scale roughness without a significant computational cost.

Slope breaks
Lava flow models often calculate flow geometry (width, thickness) locally, depending on the local slope and incoming lava flux (e.g., Harris and Rowland, 2015).However, it is possible that there might be some level of inheritance of channel structures from upslope sections to sections downslope, past a slope break (e.g., ?).This inheritance would imply, for instance, that a flow that developed a narrow channel as it travelled on a steep slope, would be narrower than expected even at more gradual terrain.The opposite can also happen, with a flow keeping a wide cross-section despite going over a break into a steeper section.Since calculations of flow advance rate depend strongly on flow width and thickness, it is important to capture the flow width accurately along the entire flow path.Conservation of flux through the channel would imply that a narrower-than-expected flow will advance faster than expected for its slope.
A recent sequence of experiments using syrup and PEG tested the hypothesis of flow width inheritance.Each liquid was extruded onto a slope that changed half-way down slope to either steeper or shallower grade.Experimental setup and overhead views of representative experiments are shown in Figure 7, and results are given in Figure 8. Experiments using isoviscous syrup showed no inheritance -the flows adjusted to the new slope instantaneously at the slope break line.Flows made of PEG showed some inheritance.
If crust formation is neglected, flow front speeds should be proportional to sine of the slope at any point (Jeffreys, 1925).For all the PEG experiments reported here, a channel forms when the flow is already in the "long-time" flow regime, dominated by downslope motion.In this situation, according to Kerr et al.
(2006) (Eqn.26 there), flow velocity U is expected to be proportional to , where ✓ is the slope.If there is no inheritance between the pre-and post-break segments, the ratio of pre-and post-break velocities should be proportional to . As shown in Figure 8a, proximal and distal flow speeds are proportional to ⇥ as expected, albeit with many variations.When plotting the speed ratio normalized by ⇥(✓ 1 )/⇥(✓ 2 ) (Figure 8b), there is no systematic correlation between the ratio of proximal to distal flow speeds and the magnitude of slope break.Therefore, a steepening or shallowing of the bed does not lead to a predictable inheritance of channel structure.This finding reassures the use of models based on the local-slope.

Remaining challenges
After many years of studying lava flows in the field, computer and laboratory, there are still many open questions, including the influence of spatial and temporal variability on the rate and extent of lava flows.As shown above, analog laboratory experiments can help scientists develop intuition and insights and construct datasets for testing simulation codes.However, several key challenges still keep us from utilizing the full power of laboratory experiments to study lava flows.

Access to 3D flow structure
One current challenge is the limited ability to collect observations, either kinematic or thermal, within the interior of laboratory flows.The 3D structure of natural flows places an important control on flow behavior, as well as provides a central post-eruption observational constraint.Thus far, experimentalists are constricted to post-experiment crosssections, which depict only the final condition and structure and no kinematic or thermal information.The threedimensional distribution of temperature is a critical constraint on lava flow evolution, for example for determining the crust thickness and strength or the possibility of internal convection.The lack of experimental observations of the interior temperatures within experiments inhibits testing of the accuracy of numerical flow models on this important aspect.In addition, experiments that are conducted under water, as is the case with PEG, complicate the collection of three-dimensional topography data using SfM or laser scanning, and prohibit the collection of thermal data using infrared cameras.
Potential approaches for handling the limited access to flow interior could include the use of specialty tracer particles.For example, photoelastic particles, made of certain glasses or polymers, can highlight the orientation of most compressive stress and indicate areas of high stress and strain within the flow (e.g., Estep and Dufek, 2012;Majmudar and Behringer, 2005).Information about the 3D thermal structure of experimental flows can be revealed using thermochromatic tracers or dyes made of materials that change color as a function of temperature.For example, an leuco dye which changes color from clear to colored at a certain temperature can highlight an isotherm within the flow.

Multiphase rheology and dynamics
Another important standing challenge in the analog modeling of lava flows is capturing the complex rheology of lava flows, and in particular the influence of the multiple phases present in natural lavas.Natural lavas contain a mix of liquid melt, solid crystals or crystal clusters, and gas bubbles, all of which influence their rheology and dynamics (Manga et al., 1998;Mader et al., 2013;Truby et al., 2015).Replicating a similar three-phase behavior in the laboratory remains a challenge.First, scaling of analog multiphase mixtures from the field to the lab is complicated by the addition of several new time and length scales.The particles and bubbles present additional length (particle and bubble size) and time (e.g., thermal conductivity or settling speed) scales to the system, as well as forces, such as surface tension or inter-particle van der Waals forces (Tsai and Zammouri, 1988).Therefore, to ensure that the experiment resides in the same dynamic regime as the natural system, these additional scales must be considered.This is necessary, for instance, in order to avoid a situation where surface tension dominated in the lab while is negligible in nature.
Creating proper mixtures of liquids, bubbles, and particles can be technically difficult.Several recent experimental techniques show potential in this area.Centrifuges can be used to remove bubbles from a viscous liquid-solids mixture (e.g., Cimarelli et al., 2011).High viscosity mixtures are more difficult to mix uniformly.Therefore a small number of residual bubbles is inevitable.They are often carefully mixed by hand (Cimarelli et al., 2011), but motorized mixers may provide the best results.The shape of particles also has an important influence on suspension rheology (Mueller et al., 2011;Moitra and Gonnermann, 2015) and suspensions with different particle shapes and sizes are achieved by using, for example, rice (Soule and Cashman, 2005), carbon fibers (Cimarelli et al., 2011), or glass fibers (Mueller et al., 2011) for prolate solid, glitter (Mueller et al., 2009(Mueller et al., , 2011) ) for oblate particles, and crushed materials for generally angular particles (Mueller et al., 2009(Mueller et al., , 2011;;Cimarelli et al., 2011).Namiki and Manga (2008); Oppenheimer (2015) and others have used a chemical reaction of citric acid and bicarbonate of soda to produce gas bubbles within a particle suspension.Phillips et al. (1995); Lane et al. (2001Lane et al. ( , 2008)); Mourtada-Bonnefoi and Mader (2004); Stix and Phillips (2012); Rivalta et al. (2013) produced bubbles by dissolving acetone in gum resin and then decompressing the material at a controlled rate.Aerators and whisks are another effective way of adding bubbles of various gases (e.g.nitrogen, air, CO2) to a suspension or a liquid (Llewellin et al., 2002;Truby et al., 2015).
New and established technologies can be utilized to characterize the mixture before, during and after experiments.For example, Magnetic Resonance Imaging (MRI) can image three-phase opaque mixtures in high temporal and spatial resolution and produce 3D maps of particle and bubble distribution within a sample or even a small analog flow (Tayler et al., 2012;Penn et al., 2017).Similarly, high-rate ultrasound transducers can produce 3D maps of acoustic wave speeds within the flow, which can be calibrated to represent local density, crystallinity, vesicularity and temperature variations (Ouriev and Windhab, 2002;Han et al., 2016).Characterizing the microstructure of analog materials used in the lab is essential to allow a quantitative comparison with the microstructure found in natural lavas.

Conclusion
Experiments using analog fluids in a laboratory setting have been a critical methodology in the study of lava flows for many years, and are likely to continue being used into the future.New experimental and data collection techniques are being introduced, providing ever more data and observations.This paper presented the fundamental concepts governing experimental lava flow simulations, reviewed popular tools and methods, as well as several new works examining, for example, flow interaction with topography.Outstanding challenges and potential ways to address those are discussed.This summary will hopefully serve to tighten the connection between numerical modelers and experimentalists.A tight collaboration between experimentalists and modelers is promised to help improve models through rigorous benchmarking and evaluation, and to advance experimental techniques by defining needs and requirements.incremental increases in height of about 5 cm to 8 cm and an original lobe height of 30 cm (Hon et al., 1994, Fig. 4c, scale as in caption).Calculating the increment of inflation divided by the original lobe height gives us values of 0.16-0.26,which, along with the Ψ values of 9.4 to 13 reported above, can be compared to experimental data on Fig. 9, where the dashed red line gives inflation increment and the blue dashed line is the percent area resurfaced.This particular lava flow plots within the region of efficient inflation, with P ranging from 0.4 to 0.5 (checkered zone).Given these P values and the reported Q avg values of 0.3-1.1 m 3 /s, we calculate Q max to be 3.1 m 3 /s.If we assume that the eruption was emplaced by a pulsating source with approximately constant frequency, we suggest that the flow experienced effusion rates 3× as high as the measured average.This method currently does not allow us to constrain the minimum eruption rate and our exper-

Conclusion
Important erup tempo, may contro Thus, it is valuable large lava fields to ucts, such as flow of the most comm appears to be enh tion requires a coh and a supply of m ments, punctuating with short pulses for inflation, and e edges of the flow fi provide conditions to 8 cm and an Fig. 4c, scale as in ivided by the origich, along with the ompared to experine gives inflation nt area resurfaced.
of efficient inflazone).Given these 1.1 m 3 /s, we calthe eruption was ately constant freeffusion rates 3× currently does not te and our exper-

Conclusion
Important eruption parameters, such as effusion rate and tempo, may control the environmental impact of large eruptions.Thus, it is valuable to link effusion rate and eruption tempo of large lava fields to the characteristics of preserved volcanic products, such as flow morphology.Here we have shown that one of the most common lava emplacement mechanisms, inflation, appears to be enhanced by pulsations in effusion rates.Inflation requires a coherent solid crust, a widespread molten core, and a supply of magma to sustain the inflation.In wax experiments, punctuating intervals of low instantaneous effusion rates with short pulses of high flux produced the conditions required for inflation, and enhanced transport of molten material to the edges of the flow field.Furthermore, such pulsating eruption rates provide conditions that favor inflation over resurfacing, which factor indicates a more irregular flow boundary geometry.A perfectly smooth oval shape will have a perimeter factor of 1.

Results
Still images of experiments are presented in Figs. 4, 5, and 6, for corn syrup, PEG, and molten basalt, respectively.Videos of experiments are available as Online Resources 1-7.Experimental results are summarized in Table 2 and displayed in Figs. 7, 8, and 9.

Corn syrup
Corn syrup experiments onto substrates with grain sizes between 0.012 and 0.10 cm (runs 3-8, Table 2) had similar symmetric, oval outlines advancing downslope from a central flow front (Fig. 4a, Online Resource 1).Experimental emplacement onto the GS = 1.0 cm substrate (runs 1 and 2, Table 2) displayed irregular outlines and advanced from multiple lobes as gravel pieces locally diverted the flow (Fig. 4b, Online Resource 2).Perimeter analysis found very similar flow shapes for each of the runs emplaced onto sandpaper, each with perimeter factors between 0.99 and 1.12 (Fig. 7, Table 2).Flows 1 and 2, both emplaced on gravel (GS = 1.0 cm), had perimeter factors of 7.03 and 5.00, respectively, representing seven and five times the complexity of the runs on surfaces with smaller grain sizes.Average flow thicknesses varied between 0.35 and 0.50 cm with no significant correlation to substrate grain size (Table 2).Maximum flow widths increased from roughly 0.2 m for all GS = 0.012 to 0.1 cm to roughly 0.4 m for GS = 1.0 cm substrate.
For corn syrup on all substrate types, downslope flow front velocities peaked immediately after initiation of the experiment and decreased with time (Fig. 9a).Initial flow velocities were greatest on the smoothest substrate (~1.1 m/s on GS = 0.012 cm) and the lowest on the roughest substrate (~0.6 cm/s on GS = 1.0 cm).At all times, flow front velocities decreased scripts.Maximum flow widths were measured from the overhead sequence images as the maximum straight-line distance of continuous material emplacement perpendicular to the downslope direction.Flow thicknesses were determined using the side view still images, by caliper after flow motion ceased for corn syrup and PEG flows, and by direct measurement of the solidified basalt during flow disassembly.In addition, we developed a perimeter factor to characterize the final shape of each flow.This factor is a ratio of the length of the perimeter squared divided by the final area of the flow normalized to the perimeter squared divided by the surface area of a perfect ellipse with the same maximum width and length as the flow.
For flows with similar width/length ratios, a higher perimeter factor indicates a more irregular flow boundary geometry.A perfectly smooth oval shape will have a perimeter factor of 1.

Results
Still images of experiments are presented in Figs. 4, 5, and 6, for corn syrup, PEG, and molten basalt, respectively.Videos of experiments are available as Online Resources 1-7.
Experimental results are summarized in Table 2 and displayed in Figs. 7, 8, and 9.

Corn syrup
Corn syrup experiments onto substrates with grain sizes between 0.012 and 0.10 cm (runs 3-8, Table 2) had similar symmetric, oval outlines advancing downslope from a central flow front (Fig. 4a, Online Resource 1).Experimental emplacement onto the GS = 1.0 cm substrate (runs 1 and 2, Table 2) displayed irregular outlines and advanced from multiple lobes as gravel pieces locally diverted the flow (Fig. 4b, Online Resource 2).Perimeter analysis found very similar flow shapes for each of the runs emplaced onto sandpaper, each with perimeter factors between 0.99 and 1.12 (Fig. 7, Table 2).Flows 1 and 2, both emplaced on gravel (GS = 1.0 cm), had perimeter factors of 7.03 and 5.00, respectively, representing seven and five times the complexity of the runs on surfaces with smaller grain sizes.Average flow thicknesses varied between 0.35 and 0.50 cm with no significant correlation to substrate grain size (Table 2).Maximum flow widths increased from roughly 0.2 m for all GS = 0.012 to 0.1 cm to roughly 0.4 m for GS = 1.0 cm substrate.
For corn syrup on all substrate types, downslope flow front velocities peaked immediately after initiation of the experiment and decreased with time (Fig. 9a).Initial flow velocities were greatest on the smoothest substrate (~1.1 m/s on GS = 0.012 cm) and the lowest on the roughest substrate (~0.6 cm/s on GS = 1.0 cm).At all times, flow front velocities decreased scripts.Maximum flow widths were measured from the overhead sequence images as the maximum straight-line distance of continuous material emplacement perpendicular to the downslope direction.Flow thicknesses were determined using the side view still images, by caliper after flow motion ceased for corn syrup and PEG flows, and by direct measurement of the solidified basalt during flow disassembly.In addition, we developed a perimeter factor to characterize the final shape of each flow.This factor is a ratio of the length of the perimeter squared divided by the final area of the flow normalized to the perimeter squared divided by the surface area of a perfect ellipse with the same maximum width and length as the flow.
For flows with similar width/length ratios, a higher perimeter factor indicates a more irregular flow boundary geometry.A perfectly smooth oval shape will have a perimeter factor of 1.

Results
Still images of experiments are presented in Figs.

Corn syrup
Corn syrup experiments onto substrates with grain sizes between 0.012 and 0.10 cm (runs 3-8, Table 2) had similar symmetric, oval outlines advancing downslope from a central flow front (Fig. 4a, Online Resource 1).Experimental emplacement onto the GS = 1.0 cm substrate (runs 1 and 2, Table 2) displayed irregular outlines and advanced from multiple lobes as gravel pieces locally diverted the flow (Fig. 4b, Online Resource 2).Perimeter analysis found very similar flow shapes for each of the runs emplaced onto sandpaper, each with perimeter factors between 0.99 and 1.12 (Fig. 7, Table 2).Flows 1 and 2, both emplaced on gravel (GS = 1.0 cm), had perimeter factors of 7.03 and 5.00, respectively, representing seven and five times the complexity of the runs on surfaces with smaller grain sizes.Average flow thicknesses varied between 0.35 and 0.50 cm with no significant correlation to substrate grain size (Table 2).Maximum flow widths increased from roughly 0.2 m for all GS = 0.012 to 0.1 cm to roughly 0.4 m for GS = 1.0 cm substrate.
For corn syrup on all substrate types, downslope flow front velocities peaked immediately after initiation of the experiment and decreased with time (Fig. 9a).Initial flow velocities were greatest on the smoothest substrate (~1.1 m/s on GS = 0.012 cm) and the lowest on the roughest substrate (~0.6 cm/s on GS = 1.0 cm).At all times, flow front velocities decreased scripts.Maximum flow widths were measured from the overhead sequence images as the maximum straight-line distance of continuous material emplacement perpendicular to the downslope direction.Flow thicknesses were determined using the side view still images, by caliper after flow motion ceased for corn syrup and PEG flows, and by direct measurement of the solidified basalt during flow disassembly.In addition, we developed a perimeter factor to characterize the final shape of each flow.This factor is a ratio of the length of the perimeter squared divided by the final area of the flow normalized to the perimeter squared divided by the surface area of a perfect ellipse with the same maximum width and length as the flow.
For flows with similar width/length ratios, a higher perimeter factor indicates a more irregular flow boundary geometry.A perfectly smooth oval shape will have a perimeter factor of 1.

Results
Still images of experiments are presented in Figs. 4, 5, and 6, for corn syrup, PEG, and molten basalt, respectively.Videos of experiments are available as Online Resources 1-7.
Experimental results are summarized in Table 2 and displayed in Figs. 7, 8, and 9.

Corn syrup
Corn syrup experiments onto substrates with grain sizes between 0.012 and 0.10 cm (runs 3-8, Table 2) had similar symmetric, oval outlines advancing downslope from a central flow front (Fig. 4a, Online Resource 1).Experimental emplacement onto the GS = 1.0 cm substrate (runs 1 and 2, Table 2) displayed irregular outlines and advanced from multiple lobes as gravel pieces locally diverted the flow (Fig. 4b, Online Resource 2).Perimeter analysis found very similar flow shapes for each of the runs emplaced onto sandpaper, each with perimeter factors between 0.99 and 1.12 (Fig. 7, Table 2).Flows 1 and 2, both emplaced on gravel (GS = 1.0 cm), had perimeter factors of 7.03 and 5.00, respectively, representing seven and five times the complexity of the runs on surfaces with smaller grain sizes.Average flow thicknesses varied between 0.35 and 0.50 cm with no significant correlation to substrate grain size (Table 2).Maximum flow widths increased from roughly 0.2 m for all GS = 0.012 to 0.1 cm to roughly 0.4 m for GS = 1.0 cm substrate.
For corn syrup on all substrate types, downslope flow front velocities peaked immediately after initiation of the experiment and decreased with time (Fig. 9a).Initial flow velocities were greatest on the smoothest substrate (~1.1 m/s on GS = 0.012 cm) and the lowest on the roughest substrate (~0.6 cm/s on GS = 1.0 cm).At all times, flow front velocities decreased   with increasing substrate grain size.This trend continued, but diminishing with time, after the initial onset of the experiments.Faster flow front advance rates led to shorter total experiment times for runs with finer substrates (Fig. 8a).

Polyethylene glycol
For all substrate types, PEG flows were oval-shaped with increasing width downslope (Fig. 5, Online Resources 3 and 4).Each flow developed lobate margins and a central levéed channel (Fig. 5) as the PEG cooled and solidified.Flows tended to advance downslope from one central flow front; however, multiple flow fronts advancing at similar rates were observed.All PEG flows had perimeter factors between 2.12 and 3.4 (Fig. 7, Table 2).There is a slight increasing trend in the perimeter factor with increasing grain size, with an average perimeter factor for flows on GS = 0.012 cm of 2.50 and an average perimeter factor for flows on GS = 1.0 cm of 3.03.Average flow thicknesses varied between 0.7 and 1.0 cm and maximum flow widths ranged from 0.29 to 0.36 m, with no correlation between flow thickness or width and GS (Table 2).
For PEG on all substrates, flow front advance rate was greatest immediately after experiment start and gradually decreased with time (Fig. 9b).Initial flow front velocities were greatest on the finest substrate (~1.5 cm/s on GS = 0.012 cm) and lowest on the coarsest substrate (~1.0 cm/s on GS = 1.0 cm).The average flow front velocities decreased as substrate grain size increased for all times.The differences between flow front velocities for the different grain-sized substrates decreased with time.Flows on the three finer substrate sizes reached their final lengths of 0.58 to 0.75 m in roughly 175 s, while the gravel substrate took ~360 s to attain final lengths of 0.68 to 0.76 m.

Molten basalt
For most substrate types, the basalt flows maintained nearly symmetric oval outlines with major axis parallel to the slope.All the flows had a ropey pāhoehoe texture and advanced downslope along a broad flow front (Fig. 6, Online Resources 5-7).Three of the six flows presented here produced breakouts near the flow front.There is a clear increase in perimeter factor with increasing grain size for the molten basalt pours (Fig. 7, Table 2).The perimeter factor is 1.11 and 1.14 for the two finest substrates (GS = 0.5 and 1.0 cm) and increases to 2.15 for the coarsest substrate (6.4 cm).The increasing complexity of the basalt flow margins with increasing grain size is distinctive in images (Fig. 6).For example, run 6 is onto a substrate with GS = 0.5 cm and displays smooth edges (Fig. 6a); run 2, onto GS = 2.9 cm, develops scalloped edges on the order of 20 cm (Fig. 6b); and flow 1, onto GS = 6.4 cm, is highly irregular with multiple breakouts in several directions and little symmetry (Fig. 6d).Average basalt flow thicknesses were scattered between 3.0 and 5.0 cm and maximum flow widths varied between 54 and 69 cm with no correlations with grain size (Table 2).with increasing substrate grain size.This trend continued, but diminishing with time, after the initial onset of the experiments.Faster flow front advance rates led to shorter total experiment times for runs with finer substrates (Fig. 8a).

Polyethylene glycol
For all substrate types, PEG flows were oval-shaped with increasing width downslope (Fig. 5, Online Resources 3 and 4).Each flow developed lobate margins and a central levéed channel (Fig. 5) as the PEG cooled and solidified.Flows tended to advance downslope from one central flow front; however, multiple flow fronts advancing at similar rates were observed.All PEG flows had perimeter factors between 2.12 and 3.4 (Fig. 7, Table 2).There is a slight increasing trend in the perimeter factor with increasing grain size, with an average perimeter factor for flows on GS = 0.012 cm of 2.50 and an average perimeter factor for flows on GS = 1.0 cm of 3.03.Average flow thicknesses varied between 0.7 and 1.0 cm and maximum flow widths ranged from 0.29 to 0.36 m, with no correlation between flow thickness or width and GS (Table 2).
For PEG on all substrates, flow front advance rate was greatest immediately after experiment start and gradually decreased with time (Fig. 9b).Initial flow front velocities were greatest on the finest substrate (~1.5 cm/s on GS = 0.012 cm) and lowest on the coarsest substrate (~1.0 cm/s on GS = 1.0 cm).The average flow front velocities decreased as substrate grain size increased for all times.The differences between flow front velocities for the different grain-sized substrates decreased with time.Flows on the three finer substrate sizes reached their final lengths of 0.58 to 0.75 m in roughly 175 s, while the gravel substrate took ~360 s to attain final lengths of 0.68 to 0.76 m.

Molten basalt
For most substrate types, the basalt flows maintained nearly symmetric oval outlines with major axis parallel to the slope.All the flows had a ropey pāhoehoe texture and advanced downslope along a broad flow front (Fig. 6, Online Resources 5-7).Three of the six flows presented here produced breakouts near the flow front.There is a clear increase in perimeter factor with increasing grain size for the molten basalt pours (Fig. 7, Table 2).The perimeter factor is 1.11 and 1.14 for the two finest substrates (GS = 0.5 and 1.0 cm) and increases to 2.15 for the coarsest substrate (6.4 cm).The increasing complexity of the basalt flow margins with increasing grain size is distinctive in images (Fig. 6).For example, run 6 is onto a substrate with GS = 0.5 cm and displays smooth edges (Fig. 6a); run 2, onto GS = 2.9 cm, develops scalloped edges on the order of 20 cm (Fig. 6b); and flow 1, onto GS = 6.4 cm, is highly irregular with multiple breakouts in several directions and little symmetry (Fig. 6d).Average basalt flow thicknesses were scattered between 3.0 and 5.0 cm and maximum flow widths varied between 54 and 69 cm with no correlations with grain size (Table 2).

Syrup PEG Basalt
factor indicates a more irregular flow boundary geometry.A perfectly smooth oval shape will have a perimeter factor of 1.

Results
Still images of experiments are presented in Figs.

Corn syrup
Corn syrup experiments onto substrates with grain sizes between 0.012 and 0.10 cm (runs 3-8, Table 2) had similar symmetric, oval outlines advancing downslope from a central flow front (Fig. 4a, Online Resource 1).Experimental emplacement onto the GS = 1.0 cm substrate (runs 1 and 2, Table 2) displayed irregular outlines and advanced from multiple lobes as gravel pieces locally diverted the flow (Fig. 4b, Online Resource 2).Perimeter analysis found very similar flow shapes for each of the runs emplaced onto sandpaper, each with perimeter factors between 0.99 and 1.12 (Fig. 7, Table 2).Flows 1 and 2, both emplaced on gravel (GS = 1.0 cm), had perimeter factors of 7.03 and 5.00, respectively, representing seven and five times the complexity of the runs on surfaces with smaller grain sizes.Average flow thicknesses varied between 0.35 and 0.50 cm with no significant correlation to substrate grain size (Table 2).Maximum flow widths increased from roughly 0.2 m for all GS = 0.012 to 0.1 cm to roughly 0.4 m for GS = 1.0 cm substrate.
For corn syrup on all substrate types, downslope flow front velocities peaked immediately after initiation of the experiment and decreased with time (Fig. 9a).Initial flow velocities were greatest on the smoothest substrate (~1.1 m/s on GS = 0.012 cm) and the lowest on the roughest substrate (~0.6 cm/s on GS = 1.0 cm).At all times, flow front velocities decreased

Figure 1 :Figure 1 .
Figure 1: Examples of a typical analog flow experimental setup.a) The basic components of an analog experimental setup include a fluid reservoir, a pump/liquid source, a tank (with cold water in the case of PEG), and cameras and sensors to document the experiment; b) A flow experiment using corn syrup at the LDEO analog fluids lab; c) A molten basalt experiment at the Syracuse Lava Lab facility.A and C are from(Rumpf et al., 2018).

Fig. 7 .
Fig. 7. Photo and chart of the height vs time showing the effect of a pulsating effusion rate.Experiments have th effusion rate with a single pause while PLS15-08 (V tot 584 cm 3 ) had 50-second between high effusion rate pulse time, illustrating the ability of the pulsed experiment to reach greater height than the steady eruption.
er et al. /Earth and Planetary Science Letters 477 (2017)  73-83  81    fect of a pulsating effusion rate.Experiments have the same Ψ value, but PLS15-15 (V tot 535 cm 3 ) had a steady m 3 ) had 50-second between high effusion rate pulses.Thin black lines show the outline of the lava flow at each ch greater height than the steady eruption.

Figure 3 :Figure 4 :
Figure 3: Pictures of experiments investigating the impact of pulsating effusion.Top row: Results from Rader et al. (2017).With everything else held the same, the dome that formed by a steady, constant rate effusion (a) exhibited a smaller thickness and less inflation than the dome that formed by pulsating effusion (b).Center and bottom rows (c-h): Overhead and side views of products of new experiments using a clay-PEG mixture with a non-Newtonian rheology.Dome surface roughness and fracturing increase with increasing episodicity, from a smooth dome that formed by constant effusion (c, d) to rougher domes that formed by sawtooth effusion rate time sequence with two peaks (e, f) and four-peaks (g, h).The average flux for all three domes was identical.

Fig. 4 Fig. 5
Fig. 4 Overhead stills of corn syrup (red) flows during experimental emplacement.a Pour 7 onto substrate with GS = 0.012 cm, image captured 142 s after experiment initialization.b Pour 1 onto substrate with GS = 1.0 cm, image captured 306 s after experiment initialization.Corn syrup was extruded from a vent on the right of image onto 7°slope.Each mark on scale bar represents 2 cm

Fig. 4 Fig. 5
Fig. 4 Overhead stills of corn syrup (red) flows during experimental emplacement.a Pour 7 onto substrate with GS = 0.012 cm, image captured 142 s after experiment initialization.b Pour 1 onto substrate with GS = 1.0 cm, image captured 306 s after experiment initialization.Corn syrup was extruded from a vent on the right of image onto 7°slope.Each mark on scale bar represents 2 cm

Fig. 4 Fig. 5
Fig. 4 Overhead stills of corn syrup (red) flows during experimental emplacement.a Pour 7 onto substrate with GS = 0.012 cm, image captured 142 s after experiment initialization.b Pour 1 onto substrate with GS = 1.0 cm, image captured 306 s after experiment initialization.Corn syrup was extruded from a vent on the right of image onto 7°slope.Each mark on scale bar represents 2 cm

Fig. 4 Fig. 5
Fig. 4 Overhead stills of corn syrup (red) flows during experimental emplacement.a Pour 7 onto substrate with GS = 0.012 cm, image captured 142 s after experiment initialization.b Pour 1 onto substrate with GS = 1.0 cm, image captured 306 s after experiment initialization.Corn syrup was extruded from a vent on the right of image onto 7°slope.Each mark on scale bar represents 2 cm

Fig. 6
Fig. 6 Overhead photographs of molten basalt flows during experimental emplacement.a Pour #6 onto substrate GS = 0.48 cm, image captured 34 s after experiment initialization.b Pour #5 onto substrate GS = 1.0 cm, image captured 83 s after experiment initialization.c Pour #2 onto substrate GS = 2.9 cm, image captured 76 s after experiment initialization.d Pour #1 onto substrate GS = 6.4 cm, image captured 70 s after experiment initialization.Basalt was poured from furnace via chute at left of images onto substrate surfaces with slopes in between 9°and 10° 63 Page 10 of 17 Bull Volcanol (2018) 80:63

Fig. 6
Fig. 6 Overhead photographs of molten basalt flows during experimental emplacement.a Pour #6 onto substrate GS = 0.48 cm, image captured 34 s after experiment initialization.b Pour #5 onto substrate GS = 1.0 cm, image captured 83 s after experiment initialization.c Pour #2 onto substrate GS = 2.9 cm, image captured 76 s after experiment initialization.d Pour #1 onto substrate GS = 6.4 cm, image captured 70 s after experiment initialization.Basalt was poured from furnace via chute at left of images onto substrate surfaces with slopes in between 9°and 10°

Fig. 4
Fig. 4 Overhead stills of corn syrup (red) flows during experimental emplacement.a Pour 7 onto substrate with GS = 0.012 cm, image captured 142 s after experiment initialization.b Pour 1 onto substrate with GS = 1.0 cm, image captured 306 s after experiment initialization.Corn syrup was extruded from a vent on the right of image onto 7°slope.Each mark on scale bar represents 2 cm

Fig. 5
Fig. 5 Overhead photographs of polyethylene glycol (PEG, green) flows during experimental emplacement.a Pour #8 onto substrate GS = 0.012 cm, image captured 160 s after experiment initialization.b Pour #2 onto substrate GS = 1.0 cm, image captured 280 s after experiment initialization.PEG was extruded from a vent on the right of image onto 7°s lope.Each mark on scale bar represents 2 cm

Figure 6 :
Figure 6: Flow front advance during analog flow experiments with varying bed roughness, from Rumpf et al. (2018).Flow materials were: A) corn syrup, B) PEG, and C) molten basalt.Circles show flow front position measured during the experiments.Solid curves show the best fitting analytical solution to flow advance (from Lister (1992)) with a given apparent viscosity.Increasing roughness grain size correlates with increasing apparent viscosity.

Figure 7 :Figure 8 :
Figure 7: Setup schematics (top row) and overhead view of resulting flow for experiments examining the influence of slope breaks on flow width and morphology.

Table 1 :
Definitions of parameters used in this paper and in the procedures for scaling laboratory experiments to natural lava flows.

Table 2 :
Classic and recent references for analog experiments studying lava flow emplacement.
4, 5, and 6, for corn syrup, PEG, and molten basalt, respectively.Videos of experiments are available as Online Resources 1-7.Experimental results are summarized in Table 2 and displayed in Figs. 7, 8, and 9.